This book provides a thorough introduction to the theory of nonlinear PDEs with a variable exponent, particularly those of elliptic type. It presents the most important variational methods for elliptic PDEs described by nonhomogeneous differential operators and containing one or more power-type nonlinearities with a variable exponent. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear elliptic equations as well as their applications to various processes arising in the applied sciences.

Isotropic and Anisotropic Function Spaces: Lebesgue and Sobolev Spaces with Variable Exponent. Variational Analysis of Problems with Variable Exponents: Nonlinear Degenerate Problems in Non-Newtonian Fluids. Spectral Theory for Differential Operators with Variable Exponent. Nonlinear Problems in Orlicz-Sobolev Spaces. Anisotropic Problems: Continuous and Discrete: Anisotropic Problems. Difference Equations with Variable Exponent. Appendices. Bibliography. Index.

Vicentiu D. Radulescu is a distinguished adjunct professor at the King Abdulaziz University of Jeddah, a professorial fellow at the "Simion Stoilow" Mathematics Institute of the Romanian Academy, and a professor of mathematics at the University of Craiova. He is the author of several books and more than 200 research papers in nonlinear analysis. He is a Highly Cited Researcher (Thomson Reuters) and a member of the Accademia Peloritana dei Pericolanti. He received his Ph.D. from the Universite Pierre et Marie Curie (Paris 6).

Dusan D. Repovs is a professor of geometry and topology at the University of Ljubljana and head of the Topology, Geometry and Nonlinear Analysis Group at the Institute of Mathematics, Physics and Mechanics in Ljubljana. He is the author of several books and more than 300 research papers in topology and nonlinear analysis. He is a member of the New York Academy of Sciences, the European Academy of Sciences, and the Engineering Academy of Slovenia. He received his Ph.D. from Florida State University.